Krishna's B.Sc. Physics Practical-II | Code 1406 | 2nd Edition

Table of contents :
B.Sc. Physics Practical-II Kumaun
Dedication
Preface
Syllabus
Brief Contents
Exp. 1: To determine the coefficient of viscosity
Exp. 2: To determine the frequency of an electrically
Exp. 3: To determine the Young's modulus (Y) by bending
Exp. 4: To determine the moment of inertia of fly wheel
Exp. 5: To determine the elastic constants by Searle'smethod
Exp. 6: To determine the magnetic field by search coil andballistic
Exp. 7: To determine the velocity of sound in a medium
Exp. 8: The draw hysteresis curve (B-H curve)
Exp. 9: To study a series resonant LCR circuit, its resonate
Exp. 10: To determine the frequency of A.C. mains

Citation preview

Krishna's

B.Sc. PHYSICS PRACTICAL-II (For B.Sc. IInd semester students) As per Kumaun University Latest Semester Syllabus w.e.f. 2016-17

By

Avinash Sharma M.Sc., P.hD. Head, Department of Physics J.L.P.G. College, Hasanpur Amroha (U.P.)

Ashok Kumar M.Sc., N.E.T. Assistant Professor J.L.P.G. College, Hasanpur Amroha (U.P.)

, KRISHNA HOUSE, 11, Shivaji Road, Meerut-250 001 (U.P.), India

Jai Shri Radhey Shyam

Dedicated to

Lord

Krishna Author & Publishers

Preface

W

e are happy to present this book entitled “B.Sc. Physics Practical-II”. It has

been written according to the Kumaun University Latest Syllabus to fulfil the requirement of B.Sc. IInd semester students.

The book is written with following special features: 1.

It is written in a simple language so that all the students may understand it easily.

2.

It has an extensive and intensive coverage of all topics.

3.

Sufficient viva-voce questions are added in this book. We are extremely grateful to our respected and beloved Parents whose

incessant inspiration guided us to accomplish this work. We also express gratitude to our family for their moral support. We are immensely thankful to Mr. S.K. Rastogi (Managing Director), Mr. Sugam Rastogi (Executive Director), Mrs. Kanupriya Rastogi (Director) and entire team of Krishna Prakashan Media (P) Ltd., for taking keen interest in this project and outstanding Management in getting the book published. The originality of the ideas is not claimed and criticism and suggestions are invited from the Students, Teaching community and other Readers.

–Authors

(vi)

Some Tips for Mixture Analysis

1

Syllabus B.Sc. PHYSICS PRACTICAL-II B.Sc. IInd Semester Kumaun University (w.e.f. 2016-2017)

List of Expt. for B.Sc. I year- Semester II (at least eight experiments which cover understanding of theory course)

Practical 1.

Viscosity of water by poissuille ’s method.

2.

Surface Tension determination.

3.

Melde ’s Experiment.

4.

Determination of modulus of rigidity (dynamical, statical method).

5.

Young ’s modules by bending of beam of known material.

6.

Elastic constants by Searle ’s method (η , γ and σ).

7.

Moment of inertia of a fly wheel.

8.

Inertia table Experiment.

9.

Determination of velocity of sound in a medium.

10.

Frequency of A.C mains (laws of vibrating strings).

11.

Torsional Oscillations (Maxwell ’s needle experiment).

12.

Determination of Ultrasonic velocity.

13.

Variation of magnetic field along the axis of a current carrying circular coil.

14.

Magnetic field determination by search coil and ballistic galvanometer.

15.

Hysteresis.

16.

Determination of self inductance/ Mutual inductance.

17.

Study of LCR circuits.

(vii)

Some Tips for Mixture Analysis

1

Brief Contents Preface.........................................................................................................(vi) Syllabus.......................................................................................................(vii) Brief Contents........................... .................................................................(viii) Exp. No. 1:

To determine the coefficient of viscosity of water by P-Poiseuille's method ......................................................(01-08)

Exp. No. 2:

To determine the frequency of an electrically maintained tuning fork using Melde's-experiment ...............................(08-13)

Exp. No. 3:

To determine the Young's modulus (Y) by bending of beam of known material .............................................(13-16)

Exp. No. 4:

To determine the moment of inertia of fly wheel .............(16-20)

Exp. No. 5:

To determine the elastic constants by Searle's method (η , Y and σ) .......................................................(20-24)

Exp. No. 6:

To determine the magnetic field by search coil and ballistic galvanometer......................................................(24-31)

Exp. No. 7:

To determine the velocity of sound in a medium ............(31-35)

Exp. No. 8:

The draw hysteresis curve (B-H curve) of a specimen in the form of a transformer on a cathode ray oscilloscope (C.R.O) and to determine its hysteresis loss..................................................................(35-38)

Exp.No. 9:

To study a series resonant LCR circuit, its resonate frequency and quality factor ............................................(38-43)

Exp. No.10: To determine the frequency of A.C. mains with the help of a sonometer.........................................................(43-48)

(viii)

1

Experiment No. -1 Object: To determine the coefficient of viscosity of water by P-Poiseuille's method. Apparatus Used: Poiseuille apparatus, a capillary tube of uniform bore, beaker, constant level water tank or a constant level device, grounded cylinder, stopwatch, meter scale, thermometer or travelling microscope.

Theory of Apparatus: A poiseuille apparatus is shown in figure. AB is long narrow capillary tube of uniform cross section, fitted horizontaly on a wooden board. This is fitted on two metallic base T1 and T2 , whose upper ends are connected with manometer by rubber tubes for measuring the pressure difference across the ends. By rubber C, we maintained the water flow. Formula and Theory: The volume of the water flowing per second slowly and steadly through a horizontal capillary tube of length l and radius a under a constant pressure difference P with a velocity below its critical speed is given as

2

or

Q=

π Pr 4 8η l

η=

πPa 4 8Ql

If h is the height of free surface of water P = hρg πhρga 4 So, η= 8Ql h → Height of water ρ → Density of water g → Gravitation constant Q → Volume of water per sec. l → Length of tube a → Radius of capillary tube Procedure: 1.

First of all, arrange the apparatus according to fig and make the capillary tube horizontal, if necessary. Also make all the ruffer joints tight so that they remain unleaked throughout the experiment. There must be no air bubble inside the apparatus.

(A) Measurement of Volume of Water Collected for Second 2.

3.

4.

5. 6.

Now allow the water from tap to run into the constant level tank and adjust its flow such that the level of water in the tank remains constant. This adjustment is done by rising and lowering the height of the tank from the capillary tube. Now with the help of pinch cock K adjust the rate of flow of water through the capillary tube such that the water emegers out from the capillary tube drop by drop and the water (or liquid) in manometer, limbs becomes stationary. Note down the steady positions of the water (of liquid) levels in the limbs of manometer and find the difference (η) in the level of water. This gives the pressure difference between the two ends of the capillary tube. Place a dry gratuated the cylinder below the exist and of the capillary tube for the collection of water and simultaneously start accurate stop watch. Collect the sufficient quantity of water for a known time t so that the volume of the water (of liquid) flowing per second through the capillary tube can be calculated. Take at least three observations of V & t for the same value of h. Now change the pressure difference h between the ends of capillary tube by rising or lowering the water and for each pressure difference repeat the above procedure for finding the volume of water collected in the gratuated cylinder per second.

3 7. 8. 9.

Take atleast four and five sets of observations for different values of pressure difference (h) and note down the temperature of water (or liquid). Plot a graph between the various value of h and their corresponding value of Q. The graph will be a straight line the slope of which gives the value of h/ Q. Measure the length of the capillary tube with the help of meter scale.

(B) Measurement of Internal Diameter of the Capillary Tube 10.

Now find the inner diameter (or radius) of the capillary tube in two mutually perpendicular directions with the help of travelling microscope in the following manner : (i)

Before taking any observation from the microscope find least count of this micrometer screw by dividing the value of one division of main scale with total number of division on vernier scale.

(ii)

Mount the capillary tube horizontally in a clamp stand and focus a travelling microscope at one of its ends as shown in figure move the microscope horizontally to one side of the fore by means of horizontal tangent screw and set the vertical cross-wire tangentially first on position A and then on B the fore. Note down the reading of the microcope at its horizontal scale in both the position A and B of the cross wire.

(iii)

Now more the microscope vertically by vertical tangent screw and adjust the horizontal Cross-wire tangentially first on position C and then on D of the bore. Note down the reading of microscope as its vertical scale in both the position C and D of the cross-wire.

(iv)

The difference of two reading of position A and B gives the internal diameter of the capillary tube in the horizontal direction and that between the two reading of position C and D gives the internal diameter of the capillary in the vertical direction.

Fig. 2

4 Observation 1.

Table (A): For the measurement of h / Q.

Least count of the stopwatch= ………… sec. Manomet- Reading Pressure er difference Water Water level in S. level in other No. one limb limb (a) (cm.) (b) (cm)

h=(a-b) (cm.)

Measurement of water collected per sec (Q) Volume of water Volume Time collected Mean of water taken per sec. value h/Q collected (t) Q (=V/t) of Q V (C.C.) (sec.) (C.C./ sec.)

1.

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(iii) —

(i)

Length of the capillary tube, L = ____ cm. Temperature of the water collected = ____ °C Density of water = ____ 1.0 gm/ cm .3

2.

Table B: For the measurement of mean radius of the capillary

Value of one division on main scale = ____ cm. Total number of division on Vernier scale = ___ div Lead count of the horizontal and vertical scale of the microscope =

Value of division on main scale Total number of division Vernier scale

= _____ cm

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Total * reading (a) (cm.)

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Main Total scale reading reading (b) (V.S.) (cm.)

Right edge of the bore

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Mean internal radius of the capillary tibe, a

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Diameter Lower edge of the bore Upper edge of the along Vernier Main direction Main Vernier Total scale scale scale reading scale X= (a-b) reading reading reading reading (a′) (cm.) (V.S.) (cm.) (V.S.) (cm.) (cm.) (M.S.) (M.S.) —

— cm.

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Mean Internal internal radius diameter of the Diameter of the bore of bore along bore capillary vertical x+y a=D/2 Total * direction D - 2 (cm.) reading y= (a-'b') (cm.) (b′) (cm.) (cm.)

Microscope reading along perpendicular direction

* Total reading= Main scale reading + number of divisions on Vernier scale coinciding with any division of main scale × least count (η×L.C)

—

Main Vernier scale scale reading reading (cm.) (V.S.) (M.S.)

Left edge of the bore

1.

S. No.

Microscope reading along any direction

5

6 Calculations 1.

Graph: The value of h / Q is calculated by plotting a graph between the values of pressure difference.

Rate of flow of liquid (Q)

l en rb u T

F

O

Pressure difference (h) (cm.)

G

lo tf

w

A Streamline flow

B C

D

h

E

Fig. 3

h along x-axis and corresponding value of water collected per second or rate of flow of liquid (or water), Q along y-axis. It will be a straight line as shown in fig 3. Find the slope of the graph which gives the value of h/Q. h  DE  = Slope of graph   =____  FG  Q Acceleration due to gravity (g) = 980 cm./sec 2 . (i)

Coefficient of viscosity of water (η), when h/Q is taken from graph η=

(ii)

πρgr 4  h    =_____ kg/m-sec. of Poise 8 l  Q

Coefficient of viscosity of water, when h/Q is taken from the observation table η=

πρgr 4 8l

h   =____ kg/m-sec. of Poise  Q

(Calculate η for each set of observations) Mean of the value of η = ____ kg/m-sec. of Poise 2.

The percentage error is the experimental result is calculated by the following formula Standard values calculated value Percentage error = × 100 Standard value = ___ %

7 Result: The result of viscosity of water at ___ °C =___ Poise Standard Result: The standard value of coefficient of viscosity of water __ at °C= ____ Poise. Percentage Error: Percentage error (%) = ___ % Precautions and Sources of Error 1.

The bore of the capillary should be narrow so that the flow of liquid in the capillary should not be turbulent.

2.

To avoid the effect of gravity of liquid the capillary tube should be placed horizontally.

3.

The bore of the capillary should be uniform.

4.

The pressure difference across the ends of the capillary should be small so that the liquid may leaves the tube drop by drop.

5.

The diameter of the tube should be measured very accurately as it occurs with 4th power in the formula.

Viva-Voce Q.1:

What are you doing?

Ans:

Sir, I am performing an experiment for the determination of coefficient of viscosity of water (or given liquid) with the help of Poiseuilla's method.

Q.2:

What a small constant pressure difference is applied across the end of the capillary tube?

Ans:

To make the flow of liquid streamline.

Q.3:

How constant pressure difference make the flow of liquid streamline?

Ans:

Constant pressure difference overcomes the viscous force acting between the differents layers of the liquid.

Q.4:

How do you apply this pressure difference in your experiment?

Ans:

It is applied by raising or lowering the water tank connected between the tap and the viscosity apparatus. Why do you use a capillarly tube of uniform radius or cross-section?

Q.5:

Ans:

To keep the flow of liquid streamline, the capillary tube should be uniform radius (or cross-section) through out. If the tube is not of uniform bore the flow the liquid becomes turbulent.

Q.6:

What happened if the capillary tube in not kept horizontally?

Ans:

If the capillary tube is not arranged in horizontal position the flow of liquid will be affected by the gravity of the earth.

8 Q.7:

Is the velocity of water flowing through the tube same everywhere?

Ans:

No, it is maximum along the axis of the tube and decreases towards the wall of the tube.

Q.8:

On what factors does the rate of flow of water through the capillarly tube depends?

Ans:

The rate of flow of water through a capillary tube depands upon the pressure difference, P the radius r and the length l of the capillary tube.

Q.9:

Can you find the viscosity of glycerine or a gas by Poiseuille's apparatus?

Ans:

No, because glycerine is highly viscous liquid. This apparatus is suitable for mobile liquids only.

Q.10:

In the critical velocity constant for every less viscous liquid?

Ans:

No, it is not constant but different for different liquid.

Experiment No. -2 Object: To determine the frequency of an electrically maintained tuning fork using Melde's- experiment. Apparatus: Electrically maintained tuning fork, pulley, thread, meter scale, pan, weight box, battery (3V), key, rheostat. Formula: For transverse mode of vibrations, n=

p 2l

T p = m 2l

Mg m

For longitudinal mode of vibrations, n=

p T p Mg = l m l m

where, n = Frequency of tuning fork. p = Number of loops. M = Mass attached to the free end of thread g = Acceleration due to gravity. m = Mass per unit length of thread used. Theory 1.

Transverse Mode Vibrations: The vibrations of the prong of the fork are in a direction perpendicular to the lenght of the string. When the frequency

9 of the waves on the string is same as that of the fork, stationary waves with well defined modes are observed. The frequency of the fork is given by, n=

p 2l

T p = m 2l

Mg m

Where p is the number of loops in the string of length l and mass per unit length m under tension T . Here T = Mg. 2.

Longitudinal Mode of Vibrations : The vibrations of the prong of the fork are along the length of the string. In this case the time during which the tuning fork completes one vibration the string completes half a vibrations. Thus the frequency of the fork, p T p Mg = l m l m

n=

Procedure Parts 1: Transverse Arrangement (i)

Make the arrangement of electrical circuit arrangement for setting vibrations in the thread by means of electrically maintained tuning fork as shown in figure. (Stationary waves are produced in the thread due to reflection at the pully. The ends of the thread where it is fixed to the prong of the tuning fork and position where it touches the pulley are modes.). l P B

Thread

M

g

M

C S –

Rh

+

E

(. )

K

Fig. 4: Electrically Maintained Tuning Fork (Transverse Arrangement)

(ii)

For this, an electric circuit is completed of an electromagnet by putting accumulates E and rheostate R in series with a tuning fork through a contact point C.

10 (iii)

By adjusting the contact point using screws, the tuning fork is set into vibrations.

(iv)

The vibrations of maximum amplitude are obtained either by adding weights (using calibrated fractional weight box) to the pan slowly in steps or by putting same mass M in the pan and the adjusting the length of the thread by moving the electrically maintained tuning fork (first opting is more convenient). The maximum amplitude of vibration is judged by putting a paper rider at its centre for a single loop for more loops. It is done simply by own judgement.

(v)

Note down the number of loops (p) formed in length l of the thread.

(vi)

Repeated the experiment for various number of loops (p).

Part 2: Longitudinal Arrangement

).(

K S

P

C

+

l

E

M –

M

R

B

Fig. 5: Longitudinal Arrangement

The longitudinal arrangement is obtained by keeping tuning fork such that motion of prongs is in the same direction as the lenght of the thread, as shown in above figure. The procedure is the same as described in part I of the experiment. Observations : 1.

Mass of the pan, w = …… gm = …… kg.

2.

Mass of 10 meter of thread = …… gm = …… kg. ∴ Mass per meter of the thread, m = …… kg./m

11 3.

Transverse Arrangement Load applied

Frequency No. of Corresponding Mean p Mg loops length of thread n = frequency 2 l m l (m) p η (Hertz) (Hertz)

S. No.

Mass kept in the pan W (kg)

Load M= W+W (kg)

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Longitudinal Arrangement Load applied

S. No.

Mass kept in the pan W (kg)

Load M= W+W (kg)

No. of loops

Corresponding length of thread l (m)

Frequency p Mg n= l m

Mean frequency η (Hertz)

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Calculations : Mass per unit length of the thread Mass = ……… kg/meter m= Length In transverse arrangement, η=

p 2l

Mg =……… c/s (or Hertz) m

Similarly calculate η for other sets of observations. In longitudinal arrangement, η=

p Mg =……… c/s or (Hertz) l m

12 Result: The frequency η of electrically maintained tuning fork, using 1.

Transverse arrangement = ……… Hz

2.

Longitudinal arrangement = ……… Hz

Standard Result: Frequency of given electrically maintained tuning fork = …… Hz % Error = ……… % Precautions and Sources of Error 1.

Mass of pan should be taken into, account for calculating load.

2.

Pulley should be frictionless.

3.

Thread should be thin, uniform and inextensible.

4.

Do not put too much load in the pan.

5.

In order to maintain l constant, mark the positions of tuning fork arrangement and that of pulley using chalk.

Viva-Voce Q.1:

What are resonant vibrations?

Ans:

It the natural frequency of a body coincides with the frequency of driving force, the former virbates with a large amplitude. Now the virbration are called as resonant vibrations.

Q.2:

When does resonance occur?

Ans:

When the natural frequency of the the rod becomes equal to the frequency of A. C. main resonance occurs.

Q.3:

Can you use a brass rod instead of a soft iron rod?

Ans:

No, because it is non magnetic.

Q.4:

What type of vibrations does the rod execute?

Ans:

The vibrations are forced vibrations. The rod executes transverse stationary vibrations of the same frequency as that of A.C.

Q.5:

Is Melde's experiment a correct method to determine the frequency of A.C. mains, as compared to other method?

Ans:

No.

13 Q.6:

Write down the formula of frequency for transverse mode of vibrations?

Ans:

Q.7:

η=

p T p = 2l m 2l

Mg m

Write down the formula of frequency for longitudinal mode of vibrations?

Ans:

η=

p T p Mg = l m l m n = Frequency of tuning fork

where,

p = Number of loops M = Mass attached to the free end of the thread. g = Gravity m = Mass per unit length of thread used. Q.8:

What is the unit of frequency?

Ans:

Hertz (Hz)

Q.9:

What is the unit of speed of sound?

Ans:

Meter/second.

Q.10:

If the radius of stretching wire is reduced to half then what will be the new wave speed compared to its initial values?

Ans:

Double.

Experiment no. - 3 Object: To determine the Young’s modulus (Y) by bending of beam of known material. Apparatus: Two knife edges , a uniform metal beam of about 1 metre long, a travelling microscope, clamping arrangement a pin, a wax, a pan with a hook, Vernier callipers, screw gauge, balance and weight box. Formula: Young’s modulus Y =

Mgh 3

4 bd 3δ Where, M= Mass attached at the centre of the beam g = Acceleration due to gravity. L = Length of the beam between two knife edges, b = Breadth of the beam d= Depth (or thickness ) of the beam, δ = Depression produced by load Mg.

14 Diagram: Mg 2

Field of view of microscope

Mg 2

S P

A

B

Mg Fig. 6

Procedure: 1. Place the knife edges about 80cm. apart by making pencil marking at the ends and support the bar on the knife edges such that it projects practically equally beyond each knife - edge and the edges are perpendicular to the length of the beam. 2. Suspend the empty pan at the C.G. of the beam and fixed a small pin vertically above the C.G. The distance of C.G. must be equal from the two knife-edges. This must be carefully noted. 3. Focus a microscope on the pin and adjust its cross–wire on pin tip and take the reading on the scale of the microscope. 4. Place a weight of M = 100 gm in the pan. The beam will bend and the pin will be lowered. Lower the microscope and make its cross-wire touch the tip again. The difference between the two reading gives the department δ, for a load of 100 gm. 5. Repeat the experiment with loads of 200, 300 , 400 g. 6. Take a second set of readings with the loads now decreasing. 7. Measure the distance between the knife-edges, also measure the breadth, b of the beam with a callipers and its thickness , d at various points with a screw gauge. M from it. 8. Draw a graph between M and δ and determine δ Observation: 1. Length between two knife–edges, L = 80 cm = 0.8 m

15 2. 3.

Breadth of the beam, b = Thickness of the beam d=

4.

Table for Depression δ: Travelling Microscope Reading Mean

Depression for 200 g δ

Mean M δ

cm

cm

cm

cm

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(3)–(1)

300

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(4)–(2)

400

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(5)–(3)

S.No.

Load M

Load increasing

Load decreasing

1.

g

cm

2.

100

3.

200

4. 5.

Calculation: M = 200 gm = 0.2 kg δ =..... cm.... m Y=

gh 3  M  =...... N / m 2 3  δ  4bd

Result: Young’s modulus for the given beam = ..............×1010 N / m 2 Precautions: 1. The knife edges should be perpendicular to the length of the beam. 2. The pan should be hung at the C.G and its distance must be equal from the two knife edges. This is important. 3. Too heavy a load, should not be used to prevent excessive bending of the beam.

Viva- voce Q.1: Ans: Q.2: Ans: Q.3: Ans: Q.4: Ans:

What do you mean by modulus of rigidity ? The ratio of the shearing stress to the shearing strain is constant for a material within the elastic limit and is known as the modulus of rigidity of the material. What is shearing stress ? It is defined as the tangential force acting per unit area of the surface. What is its unit ? In C.G.S system, its unit is dynes per square cm, whereas in M.K.S. system, it is newton/m 2 . Define Young’s modulus. It is defined as the ratio of longitudinal stress to the longitudinal strain within elastic limits. Longitudinal stress Y= Longitudinal strain

16 Q.5: Ans: Q.6: Ans:

Q.7 : Ans : Q.8: Ans: Q.9: Ans: Q.10: Ans:

Q.11: Ans:

What is Hook’s law ? This law states that within elastic limits the stress is proportional to strain i.e., stress/ strain = a constant, called modulus of elasticity. Define Bulk modulus. The ratio of normal stress to volume strain within elastic limit is called as Bulk modulus Normal stress K= Volume strain Define modulus of rigidity. It is define as the ratio of tangential stress to shearing strain within elastic limits and is denoted by η. What do you mean by beam ? A bar of uniform cross-section (circular or rectangular) whose length is much greater as compared to thickness is called a beam. What do you mean by compressibility ? − dV 1 = Compressibility = Bulk modulus VdP What is bending moment ? The moment of balancing couple (internal couple) formed by the forces of tension and compression at a section of bent beam is called as bending moment. YI Bending moment = where Y = Young’s modulus, I = Geometrical moment of R inertia and R= Radius of curvature of arc. Why have you kept the beam flat on knife edges ? Can you kept it with breadth vertical ? The depression caused by a given load, will be very small in that case.

Experiment No. -4 Object: To determine the moment of inertia of fly wheel. Apparatus: Fly wheel, the weights of about 300 and 200 g. Cotton string, stopwatch, set square, metre rod and callipers. Formula: M.I. of fly wheel is I=

2Mgh  4 πn   t 

2

n 1  1 + n 

−

Mr 2 n 1  1 + n 

Procedure : 1.

Make a loop at one end of the string and put it round the peg P, on the axle of the fly wheel tie a mass. M is other end rotate the wheel with the hand and wrap the string round the axle evenly, with no overlapping.

2.

When the weight is at A (a little below the rim) put a set-square under it and make a mark A' on the wall. (or on the side of the table).

3.

Now, let the weight descend, the string will get unwrapped as the wheel turns. The length of the string is so adjusted that when the weight rests on a

17 wooden block W (placed on the ground) the string is just tight and is on the point of slipping of peg P. A mark, ‘B’ is made at the level of B on the wall. Thus we know that when the weight will be let fall from A. It will fall through a height h = AB before getting detached from the peg. Count the rotations n 1 made by the wheel while the weight falls from A to B. This is faciliated by observing their broad mark H made on the rim as the wheel rotates. 4.

The thread is wound up agains so that the weight is at A, the block of wood is removed and the weight allowed to fall. As soon as the weight goes off the peg. Start a stopwatch count the number n of rotations made by the wheel before coming to rest (Starting from the moment the weight was detached from P) and the note the time t taken for the purpose. H P

d2

A

d1 A′

M h

B W

B′ Fig. 7

5.

Measure the diameter of the axle in two mutually perpendicular directions and determine the mean radius.

6.

Now put the weight of 200 grams on the first weight M (=300 g) and repeat the experiment.

Observations: 1.

Vernier constant of the callipers = ......cm

2.

Diameter of axle =

d1 + d2 = d =.... cm =.... m 2

∴ Mean radius of the axle = 3.

d = r cm =... m 2

Least count of the stopwatch = .....s

18 No. Rotation Clockwise  Anti Clockwise

Mass M

Height hn1

g

cm

kg

t

I

m

1

300 0.3

98.5

0.985

2

300

98.5

0.985

0.3

n

kg m2 8

198

5.00S

8

200

502 S

Average t=501 S n= 199 Clockwise  Anti Clockwise

3

500

0.5

98.5

0.985

8

--

4

500 0.5

98.5

0.985

8

----

Average t= n=

Mean I = ............ Calculations: I=

2Mgh  4 πn   l 

2

n 1  1 + n 

–

Mr 2 n 1  1 + n 

Result: Moment of inertia of the fly wheel about its axle = .......... kg. m2 Theory ...... Precautions 1.

In determining the height h the position of the bottom of the weight are to be marked on the wall in the two cases i.e., when the weight is at A and when at B.

2.

While adjusting the string, see that when the weight is resting on the block W. The string is just tight and is on the point of slipping off the peg.

3.

The timing and counting of rotations should commence from the instant the weight goes off the peg.

4.

If the wheel makes less than 100 rotations before stopping there is a consideable friction and the axle should be oiled.

5.

The diameter of the axle should be determined is two mutually perpendicular direction.

19

Viva-Voce Q.1:

What do you mean by fly wheel?

Ans:

A fly wheel is a comparatively big-sized wheel with its mass concentrated mostly in the rim.

Q.2:

What is practical use of fly wheels?

Ans:

They are fixed on the axles of moving parts of machines. They steady the motion and absorb energy when the machine tries to run faster and supply energy when it tends to slow down.

Q.3:

Give the formula for Rotational kinetic energy.

Ans:

Rotational kinetic energy is given by 1 K . E = Iω 2 2 Where I = Moment of inertia, ω = Angular speed

Q.4: Ans:

What is the moment of inertia of circular disc? 1 Moment of inertia of a circular ring I = MR 2 . Where, R is the radius of circular 2 ring.

Q.5:

What is unit of moment of inertia of a fly wheel about its axle?

Ans:

kg-m 2

Q.6:

About which axis is the moment of inertia of a body minimum?

Ans:

About the axis passing through its C.G.

Q.7:

What is the unit of M.I.?

Ans:

gm × cm 2 in C.G.S. system and newton-m 2 in M.K.S. system.

Q.8:

Can you define torque?

Ans:

The moment of a couple or the moment of force about a fixed point is called torque.

Q.9:

What is moment of inertia?

Ans:

The moment of inertia of a body about an axis is defined as the sum of the product of the mass and square of the distance of the particle from the axis of rotation. It is also equal to the torque required to produce unit angular acceleration in it about the axis.

Q.10:

Is moment of inertia constant for a body?

Ans:

No, It depends upon the mass of the body. Distribution of the mass of the body about the axis of rotation, position and direction of C.G. from the axis of rotation.

20 Q.11:

Write the mathematical form of perpendicular axis theorem?

Ans:

Iz = Ix + Iy

Q.12:

What is the theorem of parallel axes ?

Ans:

I = I C.G. + Mx 2

Q.13:

How are G and g related?

Ans:

g=

GM e Re2

, where M e is the mass of each and Re is its radius.

Experiment No. - 5 Object: To determine the elastic constants by Searle’s method (η, Y and σ). Apparatus: Searle’s arrangement (vertical stand and two identical bars), experimental wire, stopwatch, screw gauge, Vernier callipers, metre scale, physical (or spring) balance, candle, thread and matchbox. Formula: 8π l

 L2 R 2  ×M + 1  Nm −2  12 4  

1.

Y=

2.

η=

3.

σ=

Y − 1 (No unit) 2η

4.

K=

Y N/ m 2 3 (1 − 2σ)

2

r 4T1 8π l r 4T2

2

 L2 R 2  ×M + 1  Nm −2  12 4  

Description of apparatus: Figure shows the Searle’s apparatus. Two identical rods AB and CD of circular (or square) cross-section are suspended horizontally and in the same plane by two silk threads EF and GH . Which are attached to small needleholes F and H at the middle points of the rods. A short length of experimental wire FH = l has its ends passed into two into two small holes provided at F and H for the purpose. When the system is completely at rest, the bars are parallel to each other and the plane ABCD is horizontal shown in figure 8(i).

21 E

E

G

G

l A H

C

A

C

H

F l B

R D

B θ θ

(i)

D

(ii)

B

A

l

(iii) Fig. 8

Procedure: 1.

Fit up an arrangement as shown in figure 8 (i) so that AB and CD are in the same horizontal plane.

2.

Pass a cotton loop round the ends B and D and thus draw them a little towards each other. Burn the loop, the ends B and D becomes free and begin to vibrate. Note the time, t1 for 25 vibrations of the end B, thrice.

3.

Remove the two rods from the suspension set up AB horizontally, figure 8 (iii) and fix it to a rigid support. Twist CD horizontally through a small angle and determine the time t2 for 25 vibrations (looking at one end D) thrice.

4.

Measure the length of the wire and measure its diameter at a number of places in two mutually perpendicular directions at each place. Determine the mass, M of rod CD, measure its length L and radius R1.

22 Observation: 1. For Time Period: No.

No. of vibrations

Time t1 in sec

Time t 2 in sec

1.

25

.............

.............

2.

25

.............

.............

3.

25

.............

.............

Σ ′ N = 75

∴ T1 =

Σt 1 Σt , T2 = 2 ΣN ΣN

2. For Radius of Wire: Least count of the screw gauge = ............. mm

3. 4. 5. 6.

No.

Diameter along any direction in cm

Diameter along perpendicular distance direction in cm

Mean Diameter in cm

1.

.............

.............

.............

2.

.............

.............

.............

3.

.............

.............

.............

4.

.............

.............

.............

5.

.............

.............

.............

Mean diameter = ............. m Radius r = ............. m Length of wire l = ......... cm = ........... m Length of rod CD, L = ......... cm = ........... m Diameter of rod CD = .......... cm = ........... m ∴ Radius R1 of the rod CD = .......... cm = ......... m Mass of the rod CD, M = .......... gm ............. kg

Calculation: 1.

Y=

2.

η=

3.

σ=

4.

8π l 2

r 4T1 8π l r 4T2

2

 L2 R 2  ×M + 1  N/m 2  12 4    L2 R 2  ×M + 1  N/m 2  12 4  

Y −1 2η Y K= N/ m 2 3 (1 − 2σ)

23 Result: Y = .............. N/ m 2 η = .............. N/ m 2 K = ............. N/ m 2 Precautions: 1. The ends of the wire should be firmly secured into the rods. 2. The two rods AB and CD should be hang horizontal in the direction of same plane and they should be twisted through equal angles θ before being released. 3. The rods should execute torsional oscillations of small amplitude and their middle points should have the least possible movement. 4. The diameter of the wire should be determined very carefully and it should be very small as compared to its length.

Viva-Voce Q.1:

Give the name of few substances which are independent of elastic after effect.

Ans:

Quartz, phosphor-bronze, silver etc.

Q.2:

How are Y and η involved in this method ?

Ans:

First of all the wire is placed horizontally between two bars. When the bars are allowed to vibrate, the experimental wire bent into an arc. Thus the outer filaments are elongated while inner ones are contracted. In this way Y comes into play. Secondly, when one bar oscillates like a torsional pendulum, the experiment is twisted and comes into play.

Q.3:

Is the nature of vibrations the same in the second part of the experiment as in the first part?

Ans:

No, In the second case, the vibrations are torsional vibrations.

Q.4:

Should the moment of inertia of the two bars be exactly equal ?

Ans:

Yes, if the two bars are of different moment of inertia then their mean value should be used.

Q.5:

What is the value of σ for a material ?

Ans:

− 1 ≤ σ ≤ 0. 5

Q.6:

What are various relationship between elastic constants?

Ans:

Y = 2η (1 + σ), Y = 3K (1 − 2σ) σ=

2K − 2η 9 ηK ,Y= 6K + 2η η + 3K

24 Q.7:

What do you mean by Poisson’s ratio ?

Ans:

Within the elastic limits, the ratio of the lateral strain to the longitudinal strain is called Poisson’s ratio. Lateral strain σ= Longitudional strain

Q.8:

Do you prefer to use heavier or lighter bar in this experiment ?

Ans:

We shall prefer heavier bars because they have large moment of inertial. This increases the time period.

Q.9:

Can you not use thin wires in place of threads ?

Ans:

No, because during oscillations of two bars, the wires will also be twisted and their torsional reaction will affect the result.

Q.10:

What is unit of Poisson ratio ?

Ans:

Poisson ratio (σ) is a unit less quantity.

Q.11:

Give the formula for Young’s modulus. 8 πIl newton/metre 2 Y= T22 r 4

Ans:

Where,

 L2 R 2  I=M + 1   12 4  

Experiment No. - 6 Object: To determine the magnetic field by search coil and ballistic galvanometer. Apparatus Used: Search coil, Ballistic galvanometer, electromagnet, solenoid, battery, ammeter, rheostat, keys and connecting wire. Formula Used: The magnetic field B between the pole-pieces of the electromagnet is given by B=

4 π n i r2 2 10 r1

2

×

n 2 θ1 oersted. × n 1 θ2

Where, n = No. of turns per cm length in the primary of the given solenoid. n 1 = Number of turns in the search coil n 2 = Total number of turns in the secondary of the given solenoid. r1 = Radius of the search coil. r2 = Radius of the secondary of the solenoid. i = Current flowing through the primary.

25 θ 1 = First throw in the ballistic galvanometer when the search coil is suddenly removed from the space between the pole-pieces of the electromagnet. θ 2 = First throw in the ballistic galvanometer due to a current i in the primary of the solenoid. Derivation of the Formula: When a current is passed in the magnetising coils of the electromagnet, a certain field, say B is produced in the air gap between the pole-pieces. The flux linked with the search coil placed in the air cap with its face normal to the magnetic lines of force is N = n 1 AB, where n 1 is the number of turns in the search coil and A is the face area of each turn. If the search coil is suddenly removed from the space between the pole-pieces then the flux reduces to zero. dN Now induced e.m.f. e = − × 10−8 volt dt 1 dN e induced current i = = − ∴ × 10−8 amp. R R dt Where R is the effective resistance of the search coil circuit in figure 9. The total charge Q that has passed through the ballistic galvanometer coil (Which is the search coil circuit) during this time is given by t

∫

Q = i dt t

∫− 0

10−8 dN dt = R

0 0

∫−

N

N × 10−8 10−8 dN = R R

n AB = 1 × 10− 8 Coulomb R If this change produced a throw θ 1 in the ballistic galvanometer then n AB λ  × 10−8 = K θ 1 1 +  Q= 1  R 2

...(1)

Where K is the ballistic constant (in Coulomb/cm) and λ is the logarithmic decrement. Now, to eliminate K and R the connection are made as shown in figure 10. A current (say i amp) is passed through the primary of the solenoid. The magnetic  4 πni  flux linked with the secondary is   A ′ n 2 . Where n is the number of turns per  10  cm. Length of the primary, n 2 is the number of turns in the secondary and A′ is the area of cross-section of each turn of the secondary. When the current is reduced to zero.

26 This causes a charge

4 π n i A′ n2 × 10−8 Coulomb to flow through the ballistic 10 R

galvanometer coil (R is the same in both the cases). If this change produces a throw θ 2 in the galvanometer, then 10−8 ×

λ 4 π n i A′ n2  = Kθ 2  1 +   10 R 2

...(2)

Dividing equation (1) by equation (2), we get n 1 AB 10R θ × = 1 R 4 π n i A ′ n 2 θ2 B=

or

4 π n i A ′ n 2 θ1 × 10 n 1 A θ2 2

=

θ 4 π n i n 2 r2 × × 1 2 θ2 10 n 1 r1 2

Since

A = π r1

And

A ′ = π r22

Where r1 and r2 are the radii of the search coil and secondary of the solenoid respectively. Method: 1.

The ballistic galvanometer is levelled and set free. The lamp and scale arrangement is also adjusted so that a fine linear spot is formed on the scale. The initial reading of the spot, when the coil is in the rest position, is noted and adjusted at zero, If possible. The tapping key K, known as the damping key, may be used (by pressing and releasing it a no. of times in succession) to bring the coil to its position of rest quickly. The damping key will be most effective if it is pressed at the instant the spot passes through its mean position, since the rate of change of magnetic flux through the coil is maximum at this instant.

2.

Connections are first made as shown in figure 9.

3.

The search coil is placed in the air gap between the pole-pieces of the electromagnet such that its plane is normal to the magnetic lines of force or parallel to the plane of the pole-pieces.

4.

The plug key k 1 is a suitable steady current (as read by the ammeter A) is allowed to pass through the field coil of the electromagnet.

27

Fig. 9

The value of the current can be adjusted by means of the rheostat Rh in the circuit. 5.

The search coil is then suddenly removed from the gap to a considerable distance from it and the consequent first throw θ 1 in the ballistic galvanometer is noted.

6.

The experiment is repeated for different currents in the field coil.

7.

Next, the connections are made as shown in figure 10 and the rest position of the spot on the scale noted (or adjusted at zero, if possible).

8.

The key K 1 is closed. By adjusting the rheostat Rh a suitable current i amp (as read by the ameter A) is allowed to pass through the primary of solenoid.

28

Fig. 10

9.

The current in the primary is suddenly switched off by releasing the tapping key K 1 and the consequent first throw θ 2 is noted.

10.

The experiment is repeated for different currents in the primary and a graph is then plotted between the current i as absicssa and the throw θ 2 as ordinate. It comes out to be a straight line in figure. θ Whose slope gives the value of 2 . That is i θ2 i AC BC Hence = tan θ = = i θ 2 BC AC

Y B

θ2 A φ O

C i

X

Fig. 11

11.

The constants of search coil and the secondary of the solenoid are noted.

12.

The field strength B between the pole-pieces of the electromagnet is then evaluated for each value of the current in the field coil separately by using the formula given above. i is substituted from the graph. In this formula, the value of θ2

29 Observation: Observations for θ 1 when search coil is removed from the air gap between the pole-pieces of the electromagnet : Current through the field coil C amp.

Corresponding first throw θ1 cm.

1.

.............

.............

2.

.............

.............

3.

.............

.............

S. No.

Observation for the throw θ 2 when the current is switched off in the primary of the solenoid. S. No.

Current in the primary of the solenoid i amp.

Corresponding first throw θ2 cm.

i amp./cm. θ2

1.

.............

.............

.............

2.

.............

.............

.............

3.

.............

.............

.............

4.

.............

.............

.............

5.

.............

.............

.............

Calculations: Mean value of

Mean.......... i = ........ as obtained graphically or from the θ2

observation table. B=

Now

=

4 π n i r2

2

2 10 r1 2 4 π r2 × 2 10 r1

×

n 2 θ1 × n 1 θ2

n2  i  ×  × θ1 n 1  θ 2  mean

= ............ oersted. = ............ Result: Magnetising Current C amp.

Magnetic field B Oersted

..............

..............

..............

..............

..............

..............

..............

..............

30 From the table, it follows that the magnetic field depends upon the magnetising current and increases with the increase in the current. Precautions and Sources of Error: 1.

The galvanometer coil should be properly free. The base must be carefully levelled in such a way that the coil is free to move in the space between the pole pieces of the magnet and the soft iron core.

2.

Damping key K should be used only the oscillations of the coil are to be stopped. It must not be pressed while recording the values of θ 1 and θ 2 .

3.

The search coil should be placed in the air gap of the pole pieces such that its face is parallel to the face of the poles.

4.

The connections in the galvanometer circuit should be made by twin flexible wires.

5.

The search coil should be removed quickly from the air gap between the pole-pieces of the electromagnet and to a considerable distance from it.

6.

The resistance R of the galvanometer circuit should remain the same in both the parts of the experiment.

Viva-Voce Q.1:

What do you mean by the magnetic effect of current?

Ans:

When a current flows in a conductor, a magnetic field is produced around it. This is called magnetic effect of current.

Q.2:

What is the strength of magnetic field at any point on the axis of the coil?

Ans:

The magnetic field F at any point distant × from the centre of a circular coil of radius r is given by the formula F =

2 π ni r 2 10(r 2 + 42 )3 / 2

where n is the number of turns and i is the current flowing in the coil. Q.3:

What is the strength of magnetic field of the circular coil?

Ans:

The strength of the magnetic field at the centre of the coil is given by F=

2 π ni r 2 10(r 2 + 6)3 / 2

=

2 π ni 10 r

Q.4:

What is the nature of the material of the circular coil ?

Ans:

The coil is made of an insulated copper wire wound on a circular frame of non-magnetic material.

31 Q.5:

What is the direction of field at a point on the axis of the coil?

Ans:

The direction of the field is along the axis of the coil.

Q.6:

Can we use Leclanche cell for drawing the current in your experiment?

Ans:

We can not use Leclanche cell because it does not give constant current.

Q.7:

What is the use of commutator in your experiment?

Ans:

Commutator is used to reverse the direction of current in an electric circuit.

Q.8:

Why the Stewart – Gee type galvanometer is called tangent galvanometer?

Ans:

It is called tangent galvanometer because the work of this galvanometer is based upon tangent law.

Q.9:

What is the distance between two points of inflexion?

Ans:

The distance between the two points of inflexion is equal to the radius of the circular coil.

Q.10:

What is the magnitude of the magnetic field at the centre of the coil in case of tangent galvanometer?

Ans:

At the center of the coil, the magnetic field is, F=

2 π nI 10 r

Where n is the number of turns in the coil and r is the radius of coil.

Experiment No. - 7 Object: To determine the velocity of sound in a medium. Apparatus: Kundt’s tube, lycopodium powder resined leather and a meter scale. Formula: Velocity of sound in air is given by Va =

la lr

Y ρ

Where, l a = Average distance between lycopodium powder heaps in air. l r = Length of the rod, Y = Young’s modulus of the material of the rod. ρ = Density of material of rod.

32 Experiment Arrangement: B

A

M

P

D N

A

N

A

N

A

N

A

N

C lr

la Fig. 12: Kundt’s Tube

Procedure: 1.

Dry and clean the Kundt’s tube thoroughly by passing hot air and clamp it horizontally as shown in figure 12.

2.

Spread uniformly a thin layer of lycopodium powder inside the tube. Fix the tube in its proper support.

3.

Place the piston P at one end of the metal rod with the disc D on the other end of the glass tube.

4.

Clamp the rod rigidly on its middle point and make sure that the axis of the tube coinsides with the axis of the rod and is in a horizontal plane. Set the rod in longitudinal vibration by rubbing it length wise with resined leather.

5.

Adjust the position of piston P to attain the resonant condition. This can be easily judged when the lycopodium power is set into violent agitation and produces heaps at regular internals along the length of the tube.

6.

Select very carefully the positions of two extreme nodes, one near the piston P and other near the disc D and measure the distance between them using metrescale. Also count the number of spaces in between there two positions from this, calculate the average distance between two consecutive nodes.

Observations: 1.

Constants of the rod:

(i)

Length of the rod, l r = ......... cm.......m.

(ii)

Young’s modulus of the material of the rod, Y = ............ N/ m 2 .

(iii)

Density of material of the rod, ρ = ............. kg/ m 2 .

33 2.

Measurement of l a [The nodal separation of air (or gas)] S. No.

Distance between two extreme well defined heaps x (m)

Number of spaces m

Distance between two x nodes la = m

Average la (m)

1.

...........

...........

...........

...........

2.

...........

...........

...........

...........

3.

...........

...........

...........

...........

Calculations: The velocity of sound wave in air (or gas) at room temperature t = ............°C is Va = ∴

la lr

Y = ........ m/sec. ρ

Velocity of sound in air at 0°C = Va − 0 . 61 t = ............ m/sec.

Result: The velocity of sound in a dry air at 0°C = .......... m/sec. Standard Value: The standard value of velocity of sound at 0°C = 332 m/sec. Error: The percentage error = ..........% The theoretical error = ...........% Precautions: 1.

The sounding rod must be clamped rigidly exactly at its centre.

2.

The glass tube and the sounding rod should be co-axial and horizontal.

3.

The condition of resonance should be attained carefully.

4.

The tube and the lycopodium powder should be perfect fully dry as the velocity of air is affected by any trace of moisture.

34

Viva-Voce Q.1:

Why sound is heard more increase in carbon dioxide as compared to air?

Ans:

In carbon dioxide, the damping is less as compared to air.

Q.2:

Give an example of resonance in e.m. oscillations.

Ans:

Radio

Q.3:

The frequency of tuning fork is 256. Tuning forks, of which the following frequencies will be resonate it? 200, 256, 380, 512, 768, 1024

Ans:

− 256, 512, 768, 1024

Q.4:

Give two examples of sound resonance.

Ans:

Vibration of strings, Resonator.

Q.5:

Write down the formula of sound wave?

Ans:

v=

Q.6:

Speed of sound in air is not affected by:

Ans:

Pressure

Q.7:

The transverse wave cannot be produced in gases. Why?

Ans:

Gases do not have rigidity.

Q.8:

Can you hear on the earth sound of an extremely violent explosion on moon?

Ans:

No, sound can’t travel in vacuum.

Q.9:

What is the effect of temperature on the speed of sound in air?

Ans:

As the temperature of air increases, the speed of sound in air increases.

Q.10:

What is the increase in the velocity of sound in air when the temperature of air rises by 1°C?

Ans:

The velocity of sound increases by 0.61ms −1.

B ρ

35

Experiment No. -8 Object: To draw hysteresis curve (B-H curve) of a specimen in the form of a transformer on a cathode ray oscilloscope (C.R.O.) and to determine its hysteresis loss. Apparatus: Cathode ray oscilloscope (C.R.O.), specimen in the form of transformer, resistor (50 kΩ potentiometer), rheostat (10 Ω), condenser (of capacity 8 µf ), A.C. voltmeter (0-10 volts), A.C. milliammeter co-500 mA and a step down transformer. Description of C.R.O.— For the description of C.R.O. see previous experiment. Description of Circuit: The circuit used in the experiment as shown in figure 13. The secondary of the step down transformer, which converts 220 volts A.C. into 12 volts A.C. is connected in parallel to the primary of the spaciman transformer through a rheostat Rh. to measure the voltage and current flowing in the primary of the specimen an A.C. milliammeter (of rangeΘ–500mA) and voltmeter (0-10V) is connected in the primary of circuit as shown in fig. 13. A-A points of rheostat Rh and B-B points across the capacitor are connected to the pairs of Y-Y plates of the C.R.O. respectively.

220V A.C.

+

∼

P

+

P

S

S

B Y To Vertical Plan X B

A

Fig. 13 Formula Used: If a current of i amp at frequency f (50 Hz ) flows in the primary of the specimen transformer, then hysteresis loss per unit volume per cycle is given by.

36 W=

I. V. Area of the B – H curve joules/cycles f. p. Area of the rectangle

Where V be the voltage across the primary winding of the specimen transformer corresponding to current i. The area of the B-H curve is determined either by using planimeter or by placing the tracing paper on the graph of the B–H loop and by counting the small squares on their in mm. Procedure: 1.

The circuit connections are made in accordance to the fig 13.

2.

Switched on C.R.O. so that a luminious point is obtained on the screen. The intensity and focusing of the point is done with the help of their respective knobs.

3.

Apply some voltage V by means of rheostat Rh and keep the frequency selector of C.R.O. to external position. Adjust the vertical gain and horizontal gain of C.R.O. with the help of their respective gain control switches to get the proper shape and size of B-H curve on the screen. Usually the wave from obtain on screen is not for the desired shape (Fig. 14). If the shape of B-H curve is in accordance to the fig to correct them (Repeat the step no. 2 under the heading ‘‘Display of B-H curve on the screen’’).

4.

When the shape of B-H curve on C.R.O. screen becomes proper and correct, trace the curve on the tracing paper and note down the value of V and i in their respective voltmeter and millimeter.

5.

Now change the sliding position of rheostat Rh to get new value of V and i. For these new value of V and i trace the new B–H curve on the tracing paper and write V and i values on it.

6.

7.

O

Obtain various B-H curves on the screen of C.R.O. for different values of V and i adjust by rheostat. Trace corresponding B-H curves. On the tracing paper and B-H Curve also mantained on it their corresponding values of V Fig. 14 and i. Resketch all B-H curves with V and i values on a graph paper. Find the corresponding area of each B-H curve and rectangle in mm 2 .

37 Observation: S.No. Current i (mA)

Voltage V (Volts)

Area of B-H curve (mm 2)

Area of rectangle (mm 2)

1.

—

—

—

—

2.

—

—

—

—

3.

—

—

—

—

4.

—

—

—

—

5.

—

—

—

—

6.

—

—

—

—

Calculation: Hysteresis loss per unit volume per cycle for each set of observation is calculated by the formula as i. V. Area of B - H curve W= f . π. Area of rectangle = ........... joules/cycles Mean, W = .............. joules/cycles Result: The hysteresis loss of speciman transformer per unit volume per cycle is ...... joules/cycle. Precautions and Sources of Error: 1. The position of horizontal gain (Or x-amplifier) and vertical gain (or y-amplifier) should not be changed throughout the experiment once adjust. 2. Electric supply must be of constant voltage otherwise the tracing of the curve will be affected. 3. C.R.O. should be handled carefully. 4. Intensity of light on the screen should not be high.

Viva-Voce Q.1:

What are you doing?

Ans:

I am drawing hysteresis curve of ferromagnetic metarial on C.R.O.

Q.2:

What is hysteresis?

Ans:

The phenomena in which the magnetic induction B lags behind the magnatising field H during a magnetic cycle is called hysteresis.

38 Q.3:

What is retentivity?

Ans:

The retentivity of luminances is the power of a retaining a part of induced magnetism in the material causes hysteresis.

Q.4:

What do you mean by coercivity?

Ans:

The coercivity of a material is a measure of the strength of the reverse magnetising field required to wipe out the residual magnetism.

Q.5:

What do you mean by relative permeability?

Ans:

The ratio of the permeability of the medium to the permeability of air or vacuum is known as relative permeability, that is →

B µ = µr = → µ0 B0 Q.6:

What is µ 0 ?

Ans:

The absolute permeability of free space or air or vacuum µ 0 is the of the magnetic → →

flux density B0 in air or vacuum to the magnetic field strength H (i.e., B0 / H). → →

→

Q.7:

What is the relation between B, H and I ?

Ans:

→ →

→

B , H and I are related as

→

→

→

B = µ 0 (H + I )

Q.8:

What is the intensity of magnetisation?

Ans:

The intensity of magnetisation I of a magnetic field is defined as the magnetic moment per unit volume.

Q.9:

What do you mean by magnetic intensity (H ) ?

Ans:

The capability of the magnetic field to magnetise a material place in it, is expressed by means of a magnetic vector H, called the magnetic intensity of the field.

Q.10:

Why permanent magnets are made of steel?

Ans:

Because the coercivity of steel is much greater than that of iron so permanent magnets are made of steel.

→

Experiment no. -9 Object: To study a series resonant LCR circuit, its resonate frequency and quality factor. Apparatus: Inductance and capacitance of known values, resistance box preferably a decade resistance box, an AF oscillator, a step down transformer, a VTVM (or A.C. millivoltmeter or a peak detector), etc.

39 Formula: 1. 2.

Resonant frequency f r =

1 2π LC

Band width (B.W.) = ∆F = F2 − F1 =

fr Q

XL XC f = = r R R B. W . wrL 1 = = R wrCR Where, f 1 and f 2 = lower and upper half power point frequencies, w r = 2πf r where f r is resonant frequency. L = Inductance connected C = Capacitance connected R = Resistance from decade R.B.

3.

Quality factor Q =

To the LCR circuit

Fig. 15

Theory: When an alternating e.m.f. or a sinusoidal e.m.f. obtained from audio frequency oscillator (A.F.O.) is applied across a series combination of L, C, and R as shown in figure, the instantaneous voltage across the combination is given by 2  1   E = I R 2 + wL −    wc    

1/ 2

Or using j operator method, we can write  1   E = I R + j wL −    wc  1  Here R + j wL −  is the complex impedance of the circuit. Equation (2)  wc  suggests that,

40 1.

The voltages across the three components are not i phase with each other.

2.

The voltage across the inductive component is ahead of the resistive component by 90° while the voltage across the capacitive component lags behind by an equal amount of 90°.

3.

The voltages across the inductive and the capacitive components are in opposite phase i.e., 180° apart.

4.

The voltages across L and C are frequency dependent. As the frequency increases, the magnitude of the voltage across L increases, while that across C, decreases.

5.

For a given value of L and C, if the frequency is continuously change, then for a particular value of frequency say f r , known as resonant frequency, 1 we have Lw = naturally impedance of the circuit becomes minimum wc (∵ equation 2). Then w is replaced by w r = 2πf r , At resonant frequency, we have

(a) (b)

fr =

1 2π LC

and

The nature of the frequency response is determined by a factor known as quality factor Q, sometimes referred as figure of merit of the resonant circuit, which is expressed as Q=

1 w rL fr f = = = r R w r CR ( f 2 − f 1) B. W

Where the letters have their usual meaning.

100% 70.7%

B. W.

Vc

f1

f

f2

Frequency

Fig. 16

41 The value of f 1 and f 2 is obtained by calculating 70.7% of the maximum output voltage (V0 ) obtained at resonant frequency f r . The frequency response of LCR series resonant circuit is as shown in figure with band width (∆f ). Procedure: 1.

Connect the various components as shown in figure where R is the resistance box, L the given inductor, and C the capacitor. (Values of L may be of the order of say, from 100 to 1 or 8H, while values of C may be around 0.1 mF to 0.2 mF, and the series resistance is normally around few hundred of ohm).

2.

In an A.C., millivoltmeter is available in the laboratory, then the audio oscillator is not connected directly, but through a step down transformer in this case. The impedance matching transformer offers the low impedance to the circuit at resonance. Alternately a potential divider arrangement as shown in figure 16 may be used. This will offer low impedance to the circuit. But if A.C. millivoltmeter is not available, then even as a compromise if the audio oscillator is connected directly to the circuit, no serious harm would be done. The response in this case however would be flat, as the output impedance of the audio- oscillator comes in series with the circuit. With a step down transformer, the signal fed to the circuit would be about 500 MV, while it should be adjusted to about 6V to 9V without transformer. Measurement in the second case can be carried out with a peak detector or multimeter with a high input impedance.

3.

Adjust the output of the audio oscillator for an appropriate value and keep it constant throughout the experiment.

4.

Change the frequency of the audio oscillator from its lower limit say 50 Hz to the highest frequency, upto 20 kHZ, in suitable steps. For every frequency of the audio oscillator, note the output voltage Vc (= V0 ) across the capacitance C.

5.

You may repeat the experiment for different combinations of L, C and R.

Observations: For L = mH, C = ........ µF and R = ........... ohm.

42 Table for Frequency Response S.No. Frequency Hz

Input voltage Vi Output voltage V0 = Vc = constant

mA reading (A.F.)

1. 2. 3.

Calculations: A graph is plotted a semi-log paper taking frequency on logarithmic scale (X-axis) and output voltage (V0 = Vc ) on linear scale (Y-axis). The curve obtained is known as frequency response. Find 70.7% of the maximum value of V0 . Corresponding to 70.7%. draw a horizontal line, which cuts the curve at two points on both sides of fr. Note down lower cut at f 1 and upper cut at f 2 . The difference ( f 2 − f 1) Hz gives the band width. ∆f = f 2 − f 1 = ....... kHz [Experimental] From graph, fr = ....... kHz. [Experimental] ∴

Q=

fr = ........ [Experimental] B. W

Using given values of L and C: fr =

1 2π LC

Q= ∴

= ............ kHz [Calculated]

2πfrL 1 = ......... [Calculated] = ........... also Q = R 2πfr CR

Mean Q = .......... (Calculated]

Similar calculations for different combinations of L, C and R (For convenience, you may keep L and C constant and vary R only). Result: 1.

From the frequency response curve, it can be seen that for a particular value of frequency fr, the voltage Vc is maximum.

2.

The band width (∆f ) changes for various values of R. It becomes more flat when the value of R is larger/ smaller.

3.

The quality factor also depends upon R.

43 Source of Error and Precautions: 1.

Input voltage applied to the circuit, should be kept constant, throughout the experiment and it should be checked for every frequency before recording other voltages.

2.

For obtaining sharp resonance, the ration should be as high as possible.

3.

The impedance of the voltage measuring meter should be very high.

4.

Use of electrolytic capacitor should be avoided.

5.

If possible use an audio: oscillator with a low output impedance.

Experiment No. -10 Object: To determine the frequency of A.C. mains with the help of a sonometer. Apparatus Used: A.C. mains, sonometer with non-magnetic wire, a step down transformer of 6-9 volts, horse shoe magnet a set of half kg weights with hanger screw gauge and meter scale. Formula Used: The frequency of A.C. mains is given by f =

1 2l

T 1 = m 2πr

Mg πδ

Where, l = Length of sonometer wire between the two knife edges when they are adjusted for resonant vibrations. T = Tension applied to the wire M = Total mass suspended in hanger g = Acceleration due to gravity m = Mass per unit length of the sonometer wire = πr 2δ and

r = Radius of the wire.

Description of the Apparatus: The experimental arrangement is shown in figure 17. It consists of a long uniform copper wire (non-magnetic) with one end tied at the sonometer board (a long hollow wooden box). Other end passes over a frictionless pulley P and carriers a hanger H. The wire is placed between the poles of a strong horse shoe magnet NS. The magnet is kept in such a way that the

44 magnetic field is applied in a horiontal plane and at right angles to the length of the wire. The two ends of the sonometer wire are connected to secondary of the step-down transformer, to pass a small alternating current whose frequency is to be investigated.

Fig. 17

Two movable knife edges k 1 and k 2 are provided on the wooden box for stretching the wire. Usually, one knife edge is kept stationary and the second can be slided along the length of the wire to produce resonant vibration in the wire. Principle: A current carrying conductor placed in a uniform magnetic field at right angle to it is acted upon by a mechanical force (applied load), which is perpendicular to the direction of both (the current and the field). The direction of motion of the wire is given by Fleming's left hand rule. The wire is deflected due to interaction between the magnetic field and the current in the wire. As the current is alternating, the force is vertically upwards for half the cycle and vertically downward for next half cycle. Thus, the wire is acted upon by a periodic force at the frequency of the alternating current. Hence, the wire oscillates with the frequency of current and performs forced oscillations. The wire, however, has a natural frequency which can be altered by changing the distance between the knife-edges. By changing the distance between the

45 knife-edges, the natural frequency of the wire will concide with the frequency of forced vibrations (i.e., frequency of A.C. mains). Therefore, resonance will take place and wire will oscillate with a maximum amplitude. At this stage, frequency of wire is given by, f =

1 2l

T m

Where l is the length of the wire between the knife-edges, T is the tension (Applied load) in the wire and m is the mass per unit length of the wire (Qm = πr 2δ) δ is the density of the material of the wire. Procedure: 1.

Connect the primary of the step down transformer to A.C. mains, while the secondary is connected to the ends of the sonometer wire as shown in figure 17.

2.

Place the two movable sharp knife k 1, k 2 edges at the two extremities of the wooden box.

3.

The horse shoe magnet is placed vertically near the centre on the wire in such a way that the wire passes symmetrically and freely between the poles N and S of the magnet.

4.

Now, switch on the mains to pass the current in the wire. The direction of the current will then be normal to the magnetic field.

5.

Hang a suitable mass M (about 1/2 kg) on the hanger and adjust the distance between the knife edges k 1 and k 2 symmetrically with respect to the magnet till the wire vibrates with maximum amplitude (to observe resonance, place a piece of paper on the centre of the wire, the piece flies away). Note the distance (l ) between the two knife-edges.

6.

By increasing the tension (mass) in the wire, repeat step 5.

7.

Now, decrease the mass one by one from the hanger and repeat the step 5.

8.

Measure the diameter of wire at various places in mutually perpendicular directions with the help of a screw gauge and calculate the mean radius r of the wire.

9.

Note the density of the material from the table of constants.

46 Observations: 1.

Table for M and I Table 1 Mass increasing

S. No.

Mass in hanger M (gm)

Knife edge k1 (cm)

Knife edge k2 (cm)

Mass decreasing l1 = k1 – k2

Knife edge k1

Knife edge k2

l 2 = k2 – k1

(cm)

(cm)

in cm

(cm)

Mean l + l2 l= 1 2 (cm)

1. 2. 3. 4. 5.

2.

Table for the Diameter of the Wire: Value of one division of mean scale in cm Least count of screw gauge = Total number of divisions on circular scale Zero error of screw gauge = ± ..... cm Table 2 S. No.

a diam -eter (X + Y)/2 C.S. Total (cm) readi Y-ng (cm)

Reading along any Reading along perpendicular direction Θ direction O I M.S. M.S. C.S. Total X-(cm) readi read * -ng -ing read -ing

1.

...

...

...

...

...

...

...

2.

...

...

...

...

...

...

...

3.

...

...

...

...

...

...

...

4.

...

...

...

...

...

...

...

5.

...

...

...

...

...

...

...

Mean diameter d(cm)

Mean corrected diameter (if zero error occurs) d(cm)

Mean radiu -s r = (d/2) (cm)

...

...

...

C-Density of material of the wire = ..... gm/c.c. Calculations: Putting the values of M, g, δ, r and l from the observations tables in the formula i.e., 1 Mg f = = ...... c/s 2lr πδ

47 Result: The frequency of A.C. mains = ...... c/s Standard Result: The standard values of the frequecny of A.C. mains = ...... c/s Percentage Error:

Standard result (calculated result) × 100 Standard result = ............. %

Precautions and Sources of Error: 1.

The wire should be of non-magnetic substance. It should be of uniform cross-section and free of kinks.

2.

The pulley should be frictionless.

3.

The horse shoe magnet should be placed vertically in the middle of the wire with its face normal to the length of the wire.

4.

The mass loaded on the wire must include the mass of the hanger and should not cross the elastic limit of the wire.

5.

Knife edges should be moved very slowly otherwise resonance point would be missed.

48

Viva-Voce Q.1:

What are you doing?

Ans:

Sir, I am determining the frequency of A.C. mains by using sonometer method.

Q.2:

What do you mean by A.C. mains?

Ans:

The word mains stands for the main wires which are connected to the supply of current to the town. A.C. means that the current supplied by the generator is alternating current.

Q.3:

Define alternating current.

Ans:

A current which continuously varies from zero to maximum value and then again to zero and also reversing its direction at fixed interval of time, is known as alternating current.

Q.4:

What do you understand by frequency of A.C.?

Ans:

The number of times the current changes its direction in each second is called the frequency of A.C.

Q.5:

What is standard value of frequency of A.C. in India?

Ans:

Its standard value in India is 50 c/sec.

Q.6:

What is the difference between A.C. and D.C.?

Ans:

D.C. (Direct Current) does not change its direction at all, while A.C. (Alternative Current) changes its direction after a certain interval of time.

Q.7:

Does the frequency of D.C. is zero?

Ans:

Yes, the frequency of D.C. is zero.

Q.8:

What is a transformer?

Ans:

Transformer is a device for converting large current at low voltage to small current at high voltage and vice-versa.

Q.9:

Can transformer work with A.C. or D.C.?

Ans:

A transformer works with A.C. only.

Q.10:

What is the difference between step-up and step-down transformer?

Ans:

A step-up transformer is one in which the voltage level is increased while the current is decreased. The converse of this is the step-down transformer.

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